If you are trying to connect using the Cisco AnyConnect GUI client, and you are encountering an error message that appears immediately after clicking "Connect", you can get more information by exiting the app, and initiating it from the terminal.
/opt/cisco/anyconnect/bin$ ./vpnui
You may then recreate the error within the GUI, and get more diagnostic information from the terminal window.
/opt/cisco/anyconnect/bin/acwebhelper: error while loading shared libraries:
libwebkit2gtk-4.0.so.37: cannot open shared object file: No such file or directory
You should be able to resolve it by installing libwebkit2gtk-4.0-37 and restarting the vpn service.
sudo apt install libwebkit2gtk-4.0-37
This demo was in the latest Q4OS, which is based on Debian 12.
If your OS doesn't offer this version of libwebkit2gtk, other support resources may suggest manually adding repos or Ubuntu PPA, which I was expecting this demo to require before I tested it in the latest Q4OS. In that event, be cautious about adding Ubuntu PPA into Debian based systems as it could cause issues with other apps and services.